I Quantum teleportation

Quantum teleportation exploits entanglement but I don't really know how it works. And I heard that the no cloning theorem says that the original state must be destroyed. Wouldn't it violate the principle of conservation of energy mass?

I don't think there is any such violation. "Destroying" the original state doesn't mean destroying its matter. It means changing the state of the original system, in such a way that it cannot be measured again with the same result. On the receiving end, say, on Mars, the copy is made from matter on Mars; the telportation just means that that matter is put into a state that mirrors the original state of the matter on Earth.

The measurement is what "destroys" the sender's "copy" of the state. But this is a bit misleading; even if you omitted the measurement, the teleportation circuit would simply replace the sender's qubit's state with the state ##|0\rangle + |1\rangle##. There's never actually a true copy of the state.

Quantum teleportation is directionless. Nothing is transmitted from point A to B any more than from B to A. At least, not as far as any experiment can differentiate.

No, it definitely has a direction. The sender is the one doing the Bell basis measurement and broadcasting the results, and the receiver is the one applying a fixup operation based on the outcome of the measurement.

The entanglement used by teleportation is directionless, though. An EPR pair can be used to send a qubit in either direction. Also you could easily create a (more complicated and requiring more entanglement) two-way teleportation that was completely symmetric and swapped a qubit at A for a qubit at B.

No, it definitely has a direction. The sender is the one doing the Bell basis measurement and broadcasting the results, and the receiver is the one applying a fixup operation based on the outcome of the measurement. ... The entanglement used by teleportation is directionless, though. ...